In this thesis, we propose the robust control method for the synchronization of chaotic systems with unknown disturbances. We design an adaptive sliding mode controller and a sliding mode observer to synchronize chaotic systems.However, these chaotic systems are affected by unknown disturbances. With only the measured output of the chaotic system available for feedback, the observer estimates the full state and the disturbances in finite time. The adaptive sliding mode controller is designed for synchronization using estimated full state and the disturbances that is estimated by adaptive law derived from Lyapunov stability theorem. Proposed method guarantees convergence of the synchronization error to zero.